In the next sections, we
will study more a popular formula (see Appendix A,
Ref. [1]}, [2]}, [3]})
used for calculations of the fluctuations \(\omega \) ,
which is expressed in terms of the isothermal in-compressibility
\(\mathcal {K}_T\) ,
and compare the results obtained by different approximations.
Our purpose of the next sections is
to find the ranges of good agreement between the approximate expansion near
the critical point and accurate analytical result for the vdWM to check a validness of both expressions through the non-linear
susceptibility \(\chi \)  and non-linear in-compressibility
\(\mathcal {K}_T\) .
<FIGURE>